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On context semantics and interaction nets

Published: 14 July 2014 Publication History

Abstract

Context semantics is a tool inspired by Girard' s geometry of interaction. It has had many applications from study of optimal reduction to proofs of complexity bounds. Yet, context semantics have been defined only on λ-calculus and linear logic.
In order to study other languages, in particular languages with more primitives (built-in arithmetic, pattern matching,...) we define a context semantics for a broader framework: interaction nets. These are a well-behaved class of graph rewriting systems.
Here, two applications are explored. First, we define a notion of weight, based on context semantics paths, which bounds the length of reduction of nets. Then, we define a denotational semantics for a large class of interaction net systems.

References

[1]
P. Baillot, P. Coppola, and U. Dal Lago. Light logics and optimal reduction: Completeness and complexity. Information and Computation, 209(2), 2011.
[2]
P. Baillot and M. Pedicini. Elementary complexity and geometry of interaction. Fundamenta Informaticae, 45(1-2), 2001.
[3]
U Dal Lago. Context semantics, linear logic, and computational complexity. ACM Transactions on Computational Logic, 10(4), 2009.
[4]
V. Danos and L. Regnier. Proof-nets and the Hilbert space. London Mathematical Society Lecture Note Series, 1995.
[5]
M. De Falco. Géométrie de l'interaction et réseaux différentiels. These de doctorat, Université Aix-Marseille, 2, 2009.
[6]
M. Fernández and I. Mackie. Operational equivalence for interaction nets. Theoretical Computer Science, 297(1), 2003.
[7]
M. Fernández, I. Mackie, S. Sato, and M. Walker. Recursive functions with pattern matching in interaction nets. Electronic Notes in Theoretical Computer Science, 253(4), 2009.
[8]
J. Y. Girard. Proof-nets: the parallel syntax for proof-theory. Logic and Algebra, 180, 1996.
[9]
G. Gonthier, M. Abadi, and J. J. Lévy. The geometry of optimal lambda reduction. In Proceedings of the 19th ACM SIGPLAN-SIGACT symposium on Principles of programming languages. ACM, 1992.
[10]
G. Gonthier, M. Abadi, and J. J. Lévy. Linear logic without boxes. In Logic in Computer Science, 1992. LICS'92., Proceedings of the Seventh Annual IEEE Symposium on. IEEE, 1992.
[11]
Y Lafont. Interaction nets. In Principles of programming languages, 17th ACM SIGPLAN-SIGACT symposium on. ACM, 1989.
[12]
Yves Lafont. Interaction combinators. Information and Computation, 137(1), 1997.
[13]
U Dal Lago. The geometry of linear higher-order recursion. In Logic in Computer Science, 2005. LICS 2005. Proceedings. 20th Annual IEEE Symposium on. IEEE, 2005.
[14]
S. Lippi. Encoding left reduction in the lambda-calculus with interaction nets. Mathematical Structures in Computer Science, 12(6), 2002.
[15]
Damiano M. Observational equivalence and full abstraction in the symmetric interaction combinators. Logical Methods in Computer Science, 5(4:6), 2009.
[16]
I. Mackie. The geometry of interaction machine. In Ron K. Cytron and Peter Lee, editors, POPL. ACM Press, 1995.
[17]
I. Mackie and J. S. Pinto. Encoding linear logic with interaction combinators. Information and Computation, 176(2), 2002.
[18]
D. Mazza. Multiport interaction nets and concurrency. In CONCUR 2005--Concurrency Theory. Springer, 2005.
[19]
D. Mazza. Interaction nets: Semantics and concurrent extensions. These de doctorat, Université Aix-Marseille Il/Universita degli Studi Roma Tre, 2006.
[20]
M. Perrinel. On paths-based criteria for polynomial time complexity in proof-nets (long version), http://arxiv.org/abs/1201.2956, 2013.

Cited By

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  • (2020)Resource Allocation Model for a Computer SystemAETA 2019 - Recent Advances in Electrical Engineering and Related Sciences: Theory and Application10.1007/978-3-030-53021-1_50(490-500)Online publication date: 11-Aug-2020
  • (2019)Model for Resource Allocation in Decentralized Networks Using Interaction NetsApplied Informatics10.1007/978-3-030-32475-9_7(85-101)Online publication date: 28-Oct-2019
  • (2019)Interaction Net as a Representation Model of a Programming LanguageCurrent Trends in Semantic Web Technologies: Theory and Practice10.1007/978-3-030-06149-4_3(57-83)Online publication date: 18-Jan-2019
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cover image ACM Conferences
CSL-LICS '14: Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
July 2014
764 pages
ISBN:9781450328869
DOI:10.1145/2603088
  • Program Chairs:
  • Thomas Henzinger,
  • Dale Miller
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 14 July 2014

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Author Tags

  1. context semantics
  2. denotational semantics
  3. geometry of interaction
  4. interaction nets

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CSL-LICS '14 Paper Acceptance Rate 74 of 212 submissions, 35%;
Overall Acceptance Rate 215 of 622 submissions, 35%

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Cited By

View all
  • (2020)Resource Allocation Model for a Computer SystemAETA 2019 - Recent Advances in Electrical Engineering and Related Sciences: Theory and Application10.1007/978-3-030-53021-1_50(490-500)Online publication date: 11-Aug-2020
  • (2019)Model for Resource Allocation in Decentralized Networks Using Interaction NetsApplied Informatics10.1007/978-3-030-32475-9_7(85-101)Online publication date: 28-Oct-2019
  • (2019)Interaction Net as a Representation Model of a Programming LanguageCurrent Trends in Semantic Web Technologies: Theory and Practice10.1007/978-3-030-06149-4_3(57-83)Online publication date: 18-Jan-2019
  • (2018)A Programming Model for Decentralised Data NetworksApplied Computer Sciences in Engineering10.1007/978-3-030-00350-0_39(468-479)Online publication date: 13-Sep-2018
  • (2016)The complexity of interactionACM SIGPLAN Notices10.1145/2914770.283764651:1(243-255)Online publication date: 11-Jan-2016
  • (2016)The complexity of interactionProceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages10.1145/2837614.2837646(243-255)Online publication date: 11-Jan-2016

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